Question

Number of solution(s) of $2^{\sin |x|}=4^{|\cos x|}$ in $[-\pi ,\pi ]$ is equal to :

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

The total number of solutions of the given equation is equal to the number of points of intersection of curves
$2^{2|\cos x|}=2^{\sin |x|}\Rightarrow 2|\cos x|=\sin |x|$
$y=2|\cos x|,y=\sin |x|$
The given equation and final simplified equation will have same number of solutions, although the graphs may be different.


In the above graph,
Solid line curve represents graph of $\sin |x|$ and dotted line curve represents graph of $2|\cos x|$
Hence, there are $4$ solutions.